The fact that the stickiness of the KAM islands is reduced with increasing noise does not imply that they do not affect the escape dynamics in the noise-enhanced trapping. On the contrary, as it has been shown in previous works [1]}, due to the effects of noise, particles that describe escaping orbits in the deterministic system can jump into the KAM islands describing long transients. Hence, the initial decrease on the average escape time is explained by the reduction of the stickiness, but the relative maximum (i.e. the noise-enhanced trapping) is strongly related to the KAM structures. In continuous open Hamiltonian systems, changes in the physical variables due to the noise imply changes in the energy, so the particles are able to enter in the structure of the existing KAM islands for different values of the energy. However, this does not happen for every noise intensity, but only for the intensities that suit the characteristics of the fine structure of the KAM islands.
